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org.apache.commons.math3.special</FONT>
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Class Beta</H2>
<PRE>
<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
  <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math3.special.Beta</B>
</PRE>
<HR>
<DL>
<DT><PRE>public class <B>Beta</B><DT>extends <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></DL>
</PRE>

<P>
<p>
 This is a utility class that provides computation methods related to the
 Beta family of functions.
 </p>
 <p>
 Implementation of <A HREF="../../../../../org/apache/commons/math3/special/Beta.html#logBeta(double, double)"><CODE>logBeta(double, double)</CODE></A> is based on the
 algorithms described in
 <ul>
 <li><a href="http://dx.doi.org/10.1145/22721.23109">Didonato and Morris
     (1986)</a>, <em>Computation of the Incomplete Gamma Function Ratios
     and their Inverse</em>, TOMS 12(4), 377-393,</li>
 <li><a href="http://dx.doi.org/10.1145/131766.131776">Didonato and Morris
     (1992)</a>, <em>Algorithm 708: Significant Digit Computation of the
     Incomplete Beta Function Ratios</em>, TOMS 18(3), 360-373,</li>
 </ul>
 and implemented in the
 <a href="http://www.dtic.mil/docs/citations/ADA476840">NSWC Library of Mathematical Functions</a>,
 available
 <a href="http://www.ualberta.ca/CNS/RESEARCH/Software/NumericalNSWC/site.html">here</a>.
 This library is "approved for public release", and the
 <a href="http://www.dtic.mil/dtic/pdf/announcements/CopyrightGuidance.pdf">Copyright guidance</a>
 indicates that unless otherwise stated in the code, all FORTRAN functions in
 this library are license free. Since no such notice appears in the code these
 functions can safely be ported to Commons-Math.
 </p>
<P>

<P>
<DL>
<DT><B>Version:</B></DT>
  <DD>$Id: Beta.java 1420669 2012-12-12 13:40:35Z erans $</DD>
</DL>
<HR>

<P>

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<CODE>static&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/special/Beta.html#logBeta(double, double)">logBeta</A></B>(double&nbsp;p,
        double&nbsp;q)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the value of log B(p, q) for 0 ≤ x ≤ 1 and p, q > 0.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/special/Beta.html#logBeta(double, double, double, int)">logBeta</A></B>(double&nbsp;a,
        double&nbsp;b,
        double&nbsp;epsilon,
        int&nbsp;maxIterations)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<B>Deprecated.</B>&nbsp;<I>as of version 3.1, this method is deprecated as the
 computation of the beta function is no longer iterative; it will be
 removed in version 4.0. Current implementation of this method
 internally calls <A HREF="../../../../../org/apache/commons/math3/special/Beta.html#logBeta(double, double)"><CODE>logBeta(double, double)</CODE></A>.</I></TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/special/Beta.html#regularizedBeta(double, double, double)">regularizedBeta</A></B>(double&nbsp;x,
                double&nbsp;a,
                double&nbsp;b)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the
 <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html">
 regularized beta function</a> I(x, a, b).</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/special/Beta.html#regularizedBeta(double, double, double, double)">regularizedBeta</A></B>(double&nbsp;x,
                double&nbsp;a,
                double&nbsp;b,
                double&nbsp;epsilon)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the
 <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html">
 regularized beta function</a> I(x, a, b).</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/special/Beta.html#regularizedBeta(double, double, double, double, int)">regularizedBeta</A></B>(double&nbsp;x,
                double&nbsp;a,
                double&nbsp;b,
                double&nbsp;epsilon,
                int&nbsp;maxIterations)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the regularized beta function I(x, a, b).</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/special/Beta.html#regularizedBeta(double, double, double, int)">regularizedBeta</A></B>(double&nbsp;x,
                double&nbsp;a,
                double&nbsp;b,
                int&nbsp;maxIterations)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the regularized beta function I(x, a, b).</TD>
</TR>
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<TH ALIGN="left"><B>Methods inherited from class java.lang.<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></B></TH>
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<A NAME="regularizedBeta(double, double, double)"><!-- --></A><H3>
regularizedBeta</H3>
<PRE>
public static double <B>regularizedBeta</B>(double&nbsp;x,
                                     double&nbsp;a,
                                     double&nbsp;b)</PRE>
<DL>
<DD>Returns the
 <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html">
 regularized beta function</a> I(x, a, b).
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - Value.<DD><CODE>a</CODE> - Parameter <code>a</code>.<DD><CODE>b</CODE> - Parameter <code>b</code>.
<DT><B>Returns:</B><DD>the regularized beta function I(x, a, b).
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></CODE> - if the algorithm fails to converge.</DL>
</DD>
</DL>
<HR>

<A NAME="regularizedBeta(double, double, double, double)"><!-- --></A><H3>
regularizedBeta</H3>
<PRE>
public static double <B>regularizedBeta</B>(double&nbsp;x,
                                     double&nbsp;a,
                                     double&nbsp;b,
                                     double&nbsp;epsilon)</PRE>
<DL>
<DD>Returns the
 <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html">
 regularized beta function</a> I(x, a, b).
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - Value.<DD><CODE>a</CODE> - Parameter <code>a</code>.<DD><CODE>b</CODE> - Parameter <code>b</code>.<DD><CODE>epsilon</CODE> - When the absolute value of the nth item in the
 series is less than epsilon the approximation ceases to calculate
 further elements in the series.
<DT><B>Returns:</B><DD>the regularized beta function I(x, a, b)
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></CODE> - if the algorithm fails to converge.</DL>
</DD>
</DL>
<HR>

<A NAME="regularizedBeta(double, double, double, int)"><!-- --></A><H3>
regularizedBeta</H3>
<PRE>
public static double <B>regularizedBeta</B>(double&nbsp;x,
                                     double&nbsp;a,
                                     double&nbsp;b,
                                     int&nbsp;maxIterations)</PRE>
<DL>
<DD>Returns the regularized beta function I(x, a, b).
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - the value.<DD><CODE>a</CODE> - Parameter <code>a</code>.<DD><CODE>b</CODE> - Parameter <code>b</code>.<DD><CODE>maxIterations</CODE> - Maximum number of "iterations" to complete.
<DT><B>Returns:</B><DD>the regularized beta function I(x, a, b)
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></CODE> - if the algorithm fails to converge.</DL>
</DD>
</DL>
<HR>

<A NAME="regularizedBeta(double, double, double, double, int)"><!-- --></A><H3>
regularizedBeta</H3>
<PRE>
public static double <B>regularizedBeta</B>(double&nbsp;x,
                                     double&nbsp;a,
                                     double&nbsp;b,
                                     double&nbsp;epsilon,
                                     int&nbsp;maxIterations)</PRE>
<DL>
<DD>Returns the regularized beta function I(x, a, b).

 The implementation of this method is based on:
 <ul>
 <li>
 <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html">
 Regularized Beta Function</a>.</li>
 <li>
 <a href="http://functions.wolfram.com/06.21.10.0001.01">
 Regularized Beta Function</a>.</li>
 </ul>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - the value.<DD><CODE>a</CODE> - Parameter <code>a</code>.<DD><CODE>b</CODE> - Parameter <code>b</code>.<DD><CODE>epsilon</CODE> - When the absolute value of the nth item in the
 series is less than epsilon the approximation ceases to calculate
 further elements in the series.<DD><CODE>maxIterations</CODE> - Maximum number of "iterations" to complete.
<DT><B>Returns:</B><DD>the regularized beta function I(x, a, b)
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></CODE> - if the algorithm fails to converge.</DL>
</DD>
</DL>
<HR>

<A NAME="logBeta(double, double, double, int)"><!-- --></A><H3>
logBeta</H3>
<PRE>
<FONT SIZE="-1"><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Deprecated.html?is-external=true" title="class or interface in java.lang">@Deprecated</A>
</FONT>public static double <B>logBeta</B>(double&nbsp;a,
                                        double&nbsp;b,
                                        double&nbsp;epsilon,
                                        int&nbsp;maxIterations)</PRE>
<DL>
<DD><B>Deprecated.</B>&nbsp;<I>as of version 3.1, this method is deprecated as the
 computation of the beta function is no longer iterative; it will be
 removed in version 4.0. Current implementation of this method
 internally calls <A HREF="../../../../../org/apache/commons/math3/special/Beta.html#logBeta(double, double)"><CODE>logBeta(double, double)</CODE></A>.</I>
<P>
<DD>Returns the natural logarithm of the beta function B(a, b).

 The implementation of this method is based on:
 <ul>
 <li><a href="http://mathworld.wolfram.com/BetaFunction.html">
 Beta Function</a>, equation (1).</li>
 </ul>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>a</CODE> - Parameter <code>a</code>.<DD><CODE>b</CODE> - Parameter <code>b</code>.<DD><CODE>epsilon</CODE> - This parameter is ignored.<DD><CODE>maxIterations</CODE> - This parameter is ignored.
<DT><B>Returns:</B><DD>log(B(a, b)).</DL>
</DD>
</DL>
<HR>

<A NAME="logBeta(double, double)"><!-- --></A><H3>
logBeta</H3>
<PRE>
public static double <B>logBeta</B>(double&nbsp;p,
                             double&nbsp;q)</PRE>
<DL>
<DD>Returns the value of log B(p, q) for 0 ≤ x ≤ 1 and p, q > 0. Based on the
 <em>NSWC Library of Mathematics Subroutines</em> implementation,
 <code>DBETLN</code>.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>p</CODE> - First argument.<DD><CODE>q</CODE> - Second argument.
<DT><B>Returns:</B><DD>the value of <code>log(Beta(p, q))</code>, <code>NaN</code> if
 <code>p &lt;= 0</code> or <code>q &lt;= 0</code>.</DL>
</DD>
</DL>
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